Acres and square miles

There are 640 acres to the square mile. But how? The square root of 640 isn't a nice round number.

Take a square mile and divide it into an 8x8 grid, just like a chessboard. There are 64 squares in the grid and each square is 1/8 of a mile on a side, or 220 yards, or a furlong.

Now subdivide each square into 10 strips, vertical or horizontal, it doesn't matter. Each strip is an acre: 22 yards by 220 yards, or a furlong by 1/10 furlong, or a furlong by a chain.

If you recall that an acre is supposedly the amount of ground that could be ploughed in a day, this 'grid subdivided into strips' model immediately seems like a logical one, ploughing being conducted (whether with modern tractor or Anglo-Saxon horses) in long narrow strips in alternating opposite directions.